Bag of Balls

A bag contains 64 balls of eight different colours. There are eight of each colour (including red). What is the least number you would have to pick, without looking, to be sure of selecting 3 red balls?

Maybe if you wanted to know that there is a 8C2 / 64C58 = 28/74974368 = 1/2677656 (approx. 0.000000373) probability of having to pick 59 balls before getting three red balls. But as stated, this is neither a probability teaser nor an interesting teaser.